Home
Class 12
MATHS
If the length of sub-normal is equal to ...

If the length of sub-normal is equal to the length of sub-tangent at any point (3,4) on the curve `y=f(x)` and the tangent at (3,4) to `y=f(x)` meets the coordinate axes at `Aa n dB` , then the maximum area of the triangle `O A B ,` where `O` is origin, is 45/2 (b) 49/2 (c) 25/2 (d) 81/2

Promotional Banner

Topper's Solved these Questions

  • 3D COORDINATION SYSTEM

    CENGAGE PUBLICATION|Exercise DPP 3.1|11 Videos

  • APPLICATION OF INTEGRALS

    CENGAGE PUBLICATION|Exercise All Questions|143 Videos

Similar Questions

Explore conceptually related problems

If the length of subnormal is equal to length of subtangent at a point (3,4) on the curve y = f(x) and the tangent at (3,4) to y=f(x) meets the coordinate axes at A and B, then find the maximum area of the DeltaOBB wherer O is orgin

If the tangent at (1,1) on y^2=x(2-x)^2 meets the curve again at P , then find coordinates of P .

The tangent at any point P on the circle x^2+y^2=4 meets the coordinate axes at A and B . Then find the locus of the midpoint of A Bdot

Determine p such that the length of the sub-tangent and sub-normal is equal for the curve y=e^(p x)+p x at the point (0,1)dot

A variable line through the point P(2,1) meets the axes at a an d b . Find the locus of the centroid of triangle O A B (where O is the origin).

If the tangent at any point on the ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2)) =1 intersects the coordinate axes at P and Q , then the minimum value of the area (in square unit ) of the triangle OPQ is (O being the origin )-

If length of tangent at any point on the curve y=f(x) intercepted between the point and the x-axis is of length 1 . Find the equation of the curve.

Find the lengths of the tangents drawn from the point. (-4,5) to the circle x^(2)+y^(2)=16

Find the length of tangent to the curve y=4x^3-2x^5 at (-1,1)

If the tangent at any point of the curve x^((2)/(3))+y^((2)/(3))=a^((2)/(3)) meets the coordinate axes in A and B, then show that the locus of mid-points of AB is a circle.

CENGAGE PUBLICATION-APPLICATION OF DERIVATIVES-All Questions
  1. Let f be differentiable for all x , If f(1)=-2a n df^(prime)(x)geq2 fo...

    Text Solution

    |

  2. The curves 4x^2+9y^2=72 and x^2-y^2=5a t(3,2) Then (a) touch each oth...

    Text Solution

    |

  3. If the length of sub-normal is equal to the length of sub-tangent at ...

    Text Solution

    |

  4. At any point on the curve 2x^2y^2-x^4=c , the mean proportional betwee...

    Text Solution

    |

  5. The x-intercept of the tangent at any arbitrary point of the curve a/(...

    Text Solution

    |

  6. A curve is represented by the equations x=sec^2ta n dy=cott , where t ...

    Text Solution

    |

  7. The two curves x=y^2,x y=a^3 cut orthogonally at a point. Then a^2 is ...

    Text Solution

    |

  8. The line tangent to the curves y^3-x^2y+5y-2x=0 and x^2-x^3y^2+5x+2y=0...

    Text Solution

    |

  9. Tangent of acute angle between the curves y=|x^2-1| and y=sqrt(7-x^2) ...

    Text Solution

    |

  10. The number of point in the rectangle {(x , y)}-12lt=xlt=12a n d-3lt=yl...

    Text Solution

    |

  11. Consider a curve C : y=cos^(-1)(2x-1) and a straight line L :2p x-4y+2...

    Text Solution

    |

  12. Statement 1: The tangent at x=1 to the curve y=x^3-x^2-x+2 again meets...

    Text Solution

    |

  13. An aeroplane is flying horizontally at a height of 2/3k m with a veloc...

    Text Solution

    |

  14. Use the mean value theorem to prove e^(x)ge1+xAA x(inR)

    Text Solution

    |

  15. Find the condition for the line y= mx to cut at right angles the conic...

    Text Solution

    |

  16. Show that for the curve b y^2=(x+a)^3, the square of the sub-tangent v...

    Text Solution

    |

  17. Let a , b , c be three real numbers such that a < b < c f(x) is conti...

    Text Solution

    |

  18. Prove that the portion of the tangent to the curve (x+sqrt(a^2-y^2))...

    Text Solution

    |

  19. Let a , b , c be nonzero real numbers such that int0^1(1+cos^8x)(a x^2...

    Text Solution

    |

  20. If f is continuous and differentiable function and f(0)=1,f(1)=2, then...

    Text Solution

    |